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19. Аавьсet Аавьсet Аавьс. Аавьсас Аав Normal 1 No Spac. Heading! Heading 2 Tele . Font Paragraph SUMMARY OUTPUT Regression Statistics Multiple R 0.944997 R Square 0.89302 Adjusted R Square 0.875903 Standard Error 0.239984 Observations ANOVA Significance SS MIS 52.17191 8.94E-12 Regression Residual Total 4 25 29 12.01878 3.004695 1.439805 0.057592 13,45859 Intercept Price Diff Advex (AdvExp)2 AdvExp Price Diff Coefficients 29.06316 4.309083 -7.4245 0.653344 -0.55003 Standard Error Stat P-value 7.099182 4.093875 0.000389 2.667846 1.615192 0.118821 2.224741 -3.33724 0.002649 0.17411 3.752469 0.000933 0.406534 1.35297 0.188174 Upper Lower 95% 95% 14.44212 43.6842 -1.18545 9.803616 -12.0064 -2.84255 0.294757 1.011931 1 .3873 0.287243 Lower 95.0% 14.44212 1.18545 12.0064 0.294757 1.3873 Upper 95.0% 43.6842 9.803616 2.84255 1.011931 0.287243

Answer 1

11)

For the given regression model , the regression equation is defined as,

y = BoB16 +B2r3 3r+B43 e

From the regression output summary, the estimated regression equation is,

	coefficient
Intercept	29.06316
Price Diff	4.309083
AdvExp	-7.4245
(AdvExp)^2	0.653344
AdvExp*Price Diff	-0.55003

y29.06316+4.309083 x x6-7.4245x 3+0.653344 x -0.55003 x 3 Ie

12)

a)

Overall Significance

Based on the regression output summary,

Significance level = 0.05

	F	Significance F
Regression	52.17191	8.94E-12

The significance F value = 8.94E-12 which is less than 0.05 at 5% significance level which mean the model fit the data value at the predefined significance level = 0.05. Hence we can conclude that independent variables fit the model significantly compare to model when no independent variable considered.

b)

Interpretation of Independent variables

	coefficient	Interpretation
Price Diff	4.309083	For one unit increase in price difference for fresh demand will increase by 4.309083.
AdvExp	-7.4245	For one unit increase in advertisement expenditure for fresh demand will decrease by 7.4245.
(AdvExp)^2	0.653344	For one unit increase in (price difference)^2 for fresh demand will increase by 0.653344.
AdvExp*Price Diff	-0.55003	For one unit increase in AdvExp*Price Diff demand for fresh will decrease by 0.55003.

Significance of Independent variables

	coefficient	P-value		Significance level
Price Diff	4.309083	0.118821	>	0.05	Not Significant
AdvExp	-7.4245	0.002649	<	0.05	Significant
(AdvExp)^2	0.653344	0.000933	<	0.05	Significant
AdvExp*Price Diff	-0.55003	0.188174	>	0.05	Not Significant

The P-values for Price Diff and AdvExp*PriceDiff variables are greater than 0.05 at 5% significance level hence we can conclude that these independent variables are not significant in the model.

The P-values for AdvExp and (AdvExp)^2 variables are less than 0.05 at 5% significance level hence we can conclude that these independent variables are statistically significant in the model.

c)

The estimated regression equation is,

y29.06316+4.309083 x x6-7.4245x 3+0.653344 x -0.55003 x 3 Ie

13)

To compare the three different model compare the adjusted R-square value and the  R-square value. The R-square value tell, how well the regression model fit the data values. The R-square value of this model is 0.89302 which means, the model explains approximately 89.302% of the variance of the data value. So the higher value of R-square is expected for better model. And the adjusted R-square value increase if the added new variable significantly fit the data values in the model.